Solve Using the Quadratic Formula 7x^2+12x=-2

$7 x^{2} + 12 x = - 2$

Step 1

Add $2$ to both sides of the equation.

$7 x^{2} + 12 x + 2 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 7$ , $b = 12$ , and $c = 2$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (7 \cdot 2)}}{2 \cdot 7}$

Step 4

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 7 \cdot 2}}{2 \cdot 7}$

Multiply $- 4 \cdot 7 \cdot 2$ .

Multiply $- 4$ by $7$ .

$x = \frac{- 12 \pm \sqrt{144 - 28 \cdot 2}}{2 \cdot 7}$

Multiply $- 28$ by $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 56}}{2 \cdot 7}$

Subtract $56$ from $144$ .

$x = \frac{- 12 \pm \sqrt{88}}{2 \cdot 7}$

Rewrite $88$ as $2^{2} \cdot 22$ .

Factor $4$ out of $88$ .

$x = \frac{- 12 \pm \sqrt{4 (22)}}{2 \cdot 7}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{- 12 \pm \sqrt{2^{2} \cdot 22}}{2 \cdot 7}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 2 \sqrt{22}}{2 \cdot 7}$

Multiply $2$ by $7$ .

$x = \frac{- 12 \pm 2 \sqrt{22}}{14}$

Simplify $\frac{- 12 \pm 2 \sqrt{22}}{14}$ .

$x = \frac{- 6 \pm \sqrt{22}}{7}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 6 \pm \sqrt{22}}{7}$

Decimal Form:

$x = - 0.18708346 \dots, - 1.52720225 \dots$